Wreath products and the non-coprime $k(GV)$ problem

Authors

Nguyen N. Hung
Attila Maoti
Juan Martinez Madrid

Author 1 OrcID

https://orcid.org/0000-0002-5950-6271

Author 2 OrcID

https://orcid.org/0000-0002-1690-9046

Academic department

Department of Mathematics

Description

Let G = X H be the wreath product of a nontrivial finite group X with k conjugacy classes and a transitive permutation group H of degree n acting on the set of n direct factors of Xⁿ. If H is semiprimitive, then k(G) < kⁿ for every sufficiently large n or k. This result solves a case of the non-coprime k(GV) problem and provides an affirmative answer to a question of Garzoni and Gill for semiprimitive permutation groups. The proof does not require the classification of finite simple groups.

Publisher name

Cambridge University Press

Document Type

Article

Publication Date

12-28-2024

First Page

1

Last Page

17

Recommended Citation

Hung, Nguyen N.; Maoti, Attila; and Madrid, Juan Martinez, "Wreath products and the non-coprime $k(GV)$ problem" (2024). University Research. 16.
https://ideaexchange.uakron.edu/university_research/16